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Sufficient Conditions (sufficient + condition)
Kinds of Sufficient Conditions Selected AbstractsTopological Analysis of Electron Densities: Is the Presence of an Atomic Interaction Line in an Equilibrium Geometry a Sufficient Condition for the Existence of a Chemical Bond?CHEMISTRY - A EUROPEAN JOURNAL, Issue 18 2004Arne Haaland Prof. Abstract The structure, energetics, and electron density in the inclusion complex of He in adamantane, C10H16, have been studied by density functional theory calculations at the B3LYP6-311++G(2p,2d) level. Topological analysis of the electron density shows that the He atom is connected to the four tertiary tC atoms in the cage by atomic interaction lines with (3,,1) critical points. The calculated dissociation energy of the complex He@adamantane(g)=adamantane(g) + He(g) of ,E=,645 kJ,mol,1 nevertheless shows that the He,tC interactions are antibonding. [source] Multi-objective learning control for robotic manipulatorJOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 10 2004Khin Kyu Kyu Win Several types of learning controllers have been proposed in the literature to improve the tracking performance of robot manipulators. In most cases, the learning algorithms emphasize mainly on a single objective of learning a desired motion of the end-effector. In some applications, more than one objective may be specified at the same time. For example, a robot may be required to follow a desired trajectory (primary objective) and at the same time avoid an obstacle (secondary objective). Thus, multi-objective learning control can be more effective to realize the collision-free tasks. In this paper, a multi-objective learning control problem is formulated and solved. In the proposed learning control system, the primary objective is to track a desired end-effector's motion and several secondary objectives can be specified for the desired orientation and for obstacles avoidance. To avoid obstacles in the workspace, a new learning concept called "region learning control" is also proposed in this paper. The proposed learning controllers do not require the exact knowledge of robot kinematics and dynamics. Sufficient condition is presented to guarantee the convergence of the learning system. The proposed learning controllers are applied to a four-link planar redundant manipulator and simulation results are presented to illustrate the performance. © 2004 Wiley Periodicals, Inc. [source] On the stability and convergence of a Galerkin reduced order model (ROM) of compressible flow with solid wall and far-field boundary treatment,INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2010I. Kalashnikova Abstract A reduced order model (ROM) based on the proper orthogonal decomposition (POD)/Galerkin projection method is proposed as an alternative discretization of the linearized compressible Euler equations. It is shown that the numerical stability of the ROM is intimately tied to the choice of inner product used to define the Galerkin projection. For the linearized compressible Euler equations, a symmetry transformation motivates the construction of a weighted L2 inner product that guarantees certain stability bounds satisfied by the ROM. Sufficient conditions for well-posedness and stability of the present Galerkin projection method applied to a general linear hyperbolic initial boundary value problem (IBVP) are stated and proven. Well-posed and stable far-field and solid wall boundary conditions are formulated for the linearized compressible Euler ROM using these more general results. A convergence analysis employing a stable penalty-like formulation of the boundary conditions reveals that the ROM solution converges to the exact solution with refinement of both the numerical solution used to generate the ROM and of the POD basis. An a priori error estimate for the computed ROM solution is derived, and examined using a numerical test case. Published in 2010 by John Wiley & Sons, Ltd. [source] Stabilization of networked control systems with short or long random delays: A new multirate methodINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 16 2010Zhi-Hong Guan Abstract In this paper, the stabilization of a class of networked control systems (NCSs) with time-varying delay is discussed where the random delay is less than one sensor period or more than one sensor period but bounded. A new multirate method is proposed to formulate the union model for both short and long random delays. Sufficient conditions on the existence of stabilizing controllers are established when the transition probability matrix is known. V-K iteration approach is employed to calculate the mode-dependent and mode-independent state-feedback gains of NCSs. Copyright © 2009 John Wiley & Sons, Ltd. [source] Semi-global stabilization of discrete-time systems subject to non-right invertible constraintsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 11 2010Xu Wang Abstract This paper investigates time-invariant linear systems subject to input and state constraints. We study discrete-time systems with full or partial constraints on both input and state. It has been shown earlier that the solvability conditions of stabilization problems are closely related to important concepts such as the right invertibility or non-right invertibility of the constraints, the location of constraint invariant zeros, and the order of constraint infinite zeros. In this paper, for general time-invariant linear systems with non-right invertible constraints, necessary and sufficient conditions are developed under which semi-global stabilization in the admissible set can be achieved by state feedback. Sufficient conditions are also developed for such a stabilization in the case where measurement feedback is used. Such sufficient conditions are almost necessary. Controllers for both state feedback and measurement feedback are constructed as well. Copyright © 2009 John Wiley & Sons, Ltd. [source] Stability and stabilization of discrete-time singular Markov jump systems with time-varying delayINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 5 2010Shuping Ma Abstract The stochastic stability and stochastic stabilization of time-varying delay discrete-time singular Markov jump systems are discussed. For full and partial knowledge of transition probabilities cases, delay-dependent linear matrix inequalities (LMIs) conditions for the systems to be regular, causal and stochastically stable are given. Sufficient conditions are proposed for the existence of state feedback controller in terms of LMIs. Finally, two numerical examples to illustrate the effectiveness of the method are given. Copyright © 2009 John Wiley & Sons, Ltd. [source] Tracking control for sampled-data systems with uncertain time-varying sampling intervals and delaysINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 4 2010N. van de Wouw Abstract In this paper, a solution to the approximate tracking problem of sampled-data systems with uncertain, time-varying sampling intervals and delays is presented. Such time-varying sampling intervals and delays can typically occur in the field of networked control systems. The uncertain, time-varying sampling and network delays cause inexact feedforward, which induces a perturbation on the tracking error dynamics, for which a model is presented in this paper. Sufficient conditions for the input-to-state stability (ISS) of the tracking error dynamics with respect to this perturbation are given. Hereto, two analysis approaches are developed: a discrete-time approach and an approach in terms of delay impulsive differential equations. These ISS results provide bounds on the steady-state tracking error as a function of the plant properties, the control design and the network properties. Moreover, it is shown that feedforward preview can significantly improve the tracking performance and an online extremum seeking (nonlinear programming) algorithm is proposed to online estimate the optimal preview time. The results are illustrated on a mechanical motion control example showing the effectiveness of the proposed strategy and providing insight into the differences and commonalities between the two analysis approaches. Copyright © 2009 John Wiley & Sons, Ltd. [source] Design of finite-time stabilizing controllers for nonlinear dynamical systemsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 8 2009Sergey G. Nersesov Abstract Finite-time stability involves dynamical systems whose trajectories converge to an equilibrium state in finite time. Since finite-time convergence implies nonuniqueness of system solutions in reverse time, such systems possess non-Lipschitzian dynamics. Sufficient conditions for finite-time stability have been developed in the literature using Hölder continuous Lyapunov functions. In this paper, we extend the finite-time stability theory to revisit time-invariant dynamical systems and to address time-varying dynamical systems. Specifically, we develop a Lyapunov-based stability and control design framework for finite-time stability as well as finite-time tracking for time-varying nonlinear dynamical systems. Furthermore, we use the vector Lyapunov function approach to study finite-time stabilization of compact sets for large-scale dynamical systems. Copyright © 2008 John Wiley & Sons, Ltd. [source] Mixed ,2/,, nonlinear filteringINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 4 2009M. D. S. Aliyu Abstract In this paper, we consider the mixed ,2/,, filtering problem for affine nonlinear systems. Sufficient conditions for the solvability of this problem with a finite-dimensional filter are given in terms of a pair of coupled Hamilton,Jacobi,Isaacs equations (HJIEs). For linear systems, it is shown that these conditions reduce to a pair of coupled Riccati equations similar to the ones for the control case. Both the finite-horizon and the infinite-horizon problems are discussed. Simulation results are presented to show the usefulness of the scheme, and the results are generalized to include other classes of nonlinear systems. Copyright © 2008 John Wiley & Sons, Ltd. [source] Robust H, control of uncertain linear impulsive stochastic systemsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 13 2008Wu-Hua Chen Abstract This paper develops robust stability theorems and robust H, control theory for uncertain impulsive stochastic systems. The parametric uncertainties are assumed to be time varying and norm bounded. Impulsive stochastic systems can be divided into three cases, namely, the systems with stable/stabilizable continuous-time stochastic dynamics and unstable/unstabilizable discrete-time dynamics, the systems with unstable/unstabilizable continuous dynamics and stable/stabilizable discrete-time dynamics, and the systems in which both the continuous-time stochastic dynamics and the discrete-time dynamics are stable/stabilizable. Sufficient conditions for robust exponential stability and robust stabilization for uncertain impulsive stochastic systems are derived in terms of an average dwell-time condition. Then, a linear matrix inequality-based approach to the design of a robust H, controller for each system is presented. Finally, the numerical examples are provided to demonstrate the effectiveness of the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd. [source] Delay-dependent fault estimation for uncertain time-delay nonlinear systems: an LMI approachINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 18 2006Sing Kiong Nguang Abstract This paper deals with the problem of robust fault estimation for uncertain time-delay Takagi,Sugeno (TS) fuzzy models. The aim of this study is to design a delay-dependent fault estimator ensuring a prescribed ,, performance level for the fault estimation error, irrespective of the uncertainties and the time delays. Sufficient conditions for the existence of a robust fault estimator are given in terms of linear matrix inequalities (LMIs). Membership functions' (MFs) characteristics are incorporated into the fault estimator design to reduce the conservativeness of neglecting these characteristics. Finally, a numerical example is given to illustrate the effectiveness of the proposed design techniques. Copyright © 2006 John Wiley & Sons, Ltd. [source] Robust stabilizers for an implicit dynamical delay system of the neutral typeINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 4 2006D. P. GoodallArticle first published online: 28 DEC 200 Abstract A feedback stabilization problem is investigated for a class of imperfectly known implicit systems with discrete and distributed delays. The imperfections acting on the systems, which may be time-, state-, delayed state-, and/or input-dependent, are modelled as additive nonlinear perturbations influencing a known set of nonlinear functional differential equations of the neutral type. Sufficient conditions, which include a delay-dependent matrix inequality and a delay-dependent stability criterion involving some bounding parameters for the uncertainty in the system, are presented and a class of robust feedback stabilizers, including both memoryless and those with memory, are designed to guarantee a prescribed stability property for the class of implicit systems. Copyright © 2005 John Wiley & Sons, Ltd. [source] Nonlocal stabilization via delayed relay control rejecting uncertainty in a time delayINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 1 2004L. Fridman Abstract Sufficient conditions for a robust relay delayed non-local stabilization of linear systems are found, which relate the upper bound of an uncertainty in a time delay and the maximum of the real part of system spectrum. Algorithm of delayed relay control gain adaptation for non-local stabilization is suggested. The proposed algorithm suppresses bounded uncertainties in the time delay: once this relay delayed control law for the upper bound of uncertainty in the time delay for given system is designed, we ensure non-local stabilization for all values of the time delay less than the upper bound even in the case of a variable delay. Copyright © 2003 John Wiley & Sons, Ltd. [source] Robust H2 filtering of linear systems with time delaysINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 10 2003E. Fridman Abstract The problem of robust H2 estimation of a combination of states of a stationary linear system with time delays is considered. Since the problem is infinite dimensional in nature, an attempt is being made to develop finite dimensional methods that will guarantee a preassigned estimation accuracy. The approach of minimizing the trace of a matrix that overbounds the exact covariance of the estimation error is considered. Sufficient conditions are given in the form of linear matrix inequalities (LMIs). The results are illustrated by a numerical example. Copyright © 2003 John Wiley & Sons, Ltd. [source] The non-linear dynamics of output and unemployment in the U.S.JOURNAL OF APPLIED ECONOMETRICS, Issue 4 2001Filippo Altissimo This paper studies the joint dynamics of U.S. output and unemployment rate in a non-linear VAR model. The non-linearity is introduced through a feedback variable that endogenously augments the output lags of the VAR in recessionary phases. Sufficient conditions for the ergodicity of the model, potentially applying to a larger class of threshold models, are provided. The linear specification is rejected in favour of our threshold VAR. However, in the estimation the feedback is found to be statistically significant only on unemployment, while it transmits to output through its cross-correlation. This feedback effect from recessions generates important asymmetries in the propagation of shocks, a possible key to interpret the divergence in the measures of persistence in the literature. The regime-dependent persistence also explains the finding that the feedback from recession exerts a positive effect on the long-run growth rate of the economy, an empirical validation of the Schumpeterian macroeconomic theories. Copyright © 2001 John Wiley & Sons, Ltd. [source] Sufficient conditions for graphs to be ,,-optimal, super-edge-connected, and maximally edge-connectedJOURNAL OF GRAPH THEORY, Issue 3 2005Angelika Hellwig Abstract The restricted-edge-connectivity of a graph G, denoted by ,,(G), is defined as the minimum cardinality over all edge-cuts S of G, where G - S contains no isolated vertices. The graph G is called ,,-optimal, if ,,(G),=,,(G), where ,(G) is the minimum edge-degree in G. A graph is super-edge-connected, if every minimum edge-cut consists of edges adjacent to a vertex of minimum degree. In this paper, we present sufficient conditions for arbitrary, triangle-free, and bipartite graphs to be ,,-optimal, as well as conditions depending on the clique number. These conditions imply super-edge-connectivity, if , (G),,,3, and the equality of edge-connectivity and minimum degree. Different examples will show that these conditions are best possible and independent of other results in this area. © 2005 Wiley Periodicals, Inc. J Graph Theory 48: 228,246, 2005 [source] Decomposing kernels of iterated operators,a unified approachMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 9 2007Guangbin Ren Abstract For any operator D acting in an Abelian group, we study the kernel of its iterates Dk and describe a general approach for decomposing it through the kernel of the operator D itself and some other given operators T1,,,Tk,1. Due to Almansi's famous theorem for polyharmonic functions the different types of decomposition are characterized in terms of strong, weak and restricted Almansi decomposition properties. Sufficient conditions are given for the existence of such decompositions. The case of the iterated Dirac operator (cf. Math. Meth. Appl. Sci. 2002; 25:1541,1552) follows as a special case. Several other special cases are discussed. Finally we prove corresponding decomposition theorems for the iterated weighted Laplacian (|x|,,)k, ,,(,,, 2), and the iterated Helmholtz type operator (,,,)k, ,,C. Copyright © 2006 John Wiley & Sons, Ltd. [source] Sufficient conditions of non-uniqueness for the Coulomb friction problemMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 1 2004Riad Hassani Abstract We consider the Signorini problem with Coulomb friction in elasticity. Sufficient conditions of non-uniqueness are obtained for the continuous model. These conditions are linked to the existence of real eigenvalues of an operator in a Hilbert space. We prove that, under appropriate conditions, real eigenvalues exist for a non-local Coulomb friction model. Finite element approximation of the eigenvalue problem is considered and numerical experiments are performed. Copyright © 2003 John Wiley & Sons, Ltd. [source] Solutions of Volterra integral equations with infinite delayMATHEMATISCHE NACHRICHTEN, Issue 3 2008Daniel Franco Abstract We present several new existence results for a Volterra integral equation with infinite delay. We discuss periodic and bounded solutions. Sufficient conditions for the existence of positive periodic solutions are also provided. The techniques we employ have not been used for this equation before. Our results generalize and complement those in the literature and several examples are presented to show their applicability. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Pseudodifferential operators with compound non-regular symbolsMATHEMATISCHE NACHRICHTEN, Issue 9-10 2007Yu. I. Karlovich Abstract Let V (,) denote the Banach algebra of absolutely continuous functions of bounded total variation on ,. We study an algebra ,, of pseudodifferential operators of zero order with compound slowly oscillating V (,)-valued symbols (x, y) , a (x, y, ·) that satisfy a Lipschitz condition with respect to the spatial variables x, y , ,. Sufficient conditions for the boundedness and compactness of pseudodifferential operators with compound symbols on the Lebesgue spaces Lp(,), for p = 2 and 1 < p < ,, are obtained. A Fredholm criterion and an index formula for pseudodifferential operators A , ,, are presented. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Sufficient conditions for a graph to be super restricted edge-connectedNETWORKS: AN INTERNATIONAL JOURNAL, Issue 3 2008Shiying Wang Abstract Restricted edge connectivity is a more refined network reliability index than edge connectivity. A restricted edge cut F of a connected graph G is an edge cut such that G - F has no isolated vertex. The restricted edge connectivity ,, is the minimum cardinality over all restricted edge cuts. We call G ,,-optimal if ,, = ,, where , is the minimum edge degree in G. Moreover, a ,,-optimal graph G is called a super restricted edge-connected graph if every minimum restricted edge cut separates exactly one edge. Let D and g denote the diameter and girth of G, respectively. In this paper, we first present a necessary condition for non-super restricted edge-connected graphs with minimum degree , , 3 and D , g , 2. Next, we prove that a connected graph with minimum degree , , 3 and D , g , 3 is super restricted edge-connected. Finally, we give some sufficient conditions on the conditional diameter and the girth for super restricted edge-connected graphs. © 2007 Wiley Periodicals, Inc. NETWORKS, 2008 [source] Numerical methods for fourth-order nonlinear elliptic boundary value problemsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2001C. V. Pao Abstract The aim of this article is to present several computational algorithms for numerical solutions of a nonlinear finite difference system that represents a finite difference approximation of a class of fourth-order elliptic boundary value problems. The numerical algorithms are based on the method of upper and lower solutions and its associated monotone iterations. Three linear monotone iterative schemes are given, and each iterative scheme yields two sequences, which converge monotonically from above and below, respectively, to a maximal solution and a minimal solution of the finite difference system. This monotone convergence property leads to upper and lower bounds of the solution in each iteration as well as an existence-comparison theorem for the finite difference system. Sufficient conditions for the uniqueness of the solution and some techniques for the construction of upper and lower solutions are obtained, and numerical results for a two-point boundary-value problem with known analytical solution are given. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17:347,368, 2001 [source] Dynamic advertising with spillovers: Cartel vs competitive fringeOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 6 2009Luca Lambertini Abstract A differential oligopoly game with advertising is investigated, where different dynamics occur between two groups of agents, the former playing a competitive Nash game and the latter cooperating as a cartel. Sufficient conditions for stability and a qualitative analysis of the profit ratio and social welfare at equilibrium are provided. A threshold value for the size of the competitive fringe is pointed out by a suitable numerical simulation. Copyright © 2009 John Wiley & Sons, Ltd. [source] ,, control of discrete-time Markov jump systems with bounded transition probabilitiesOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 5 2009E. K. Boukas Abstract This paper deals with the class of discrete-time linear systems with random abrupt changes and unknown transition probabilities but varying between known bounds for each mode. The ,, control problem of this class of systems is revisited and new sufficient conditions are developed in the linear matrix inequality (LMI) setting to design the state-feedback controller that stochastically stabilizes the system under consideration and at the same time guarantees the disturbance rejection with a desired level , . Sufficient conditions for existence of the state-feedback controller are developed. It is shown that the addressed problem can be solved if the corresponding developed LMIs are feasible. Numerical examples are employed to show the usefulness of the proposed results. Copyright © 2008 John Wiley & Sons, Ltd. [source] Stability of some exact solutions of the shallow-water equations for testing numerical models in spherical geometryTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 632 2008A. Staniforth Abstract Five families of exact axisymmetric solutions of the nonlinear shallow-water equations in spherical geometry have recently been proposed as an aid to the development and testing of global numerical models. Sufficient conditions for the stability of these solutions are here derived to guide the choice of values for the family parameters. Thus it can be ensured that any significant time evolution occurring in a numerical model initialised with one of these exact solutions is of numerical origin, and does not reflect an inherent physical instability. With the caveat that only sufficient conditions for stability are examined, it appears that planetary rotation stabilises the solutions (as would be so if the flow were governed by barotropic vorticity dynamics), and that low Rossby and Froude numbers favour their stability. © Crown Copyright 2008. Reproduced with the permission of the Controller of HMSO. Published by John Wiley & Sons, Ltd [source] On the weak IFR aging of bivariate lifetime distributionsAPPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 3 2005Maxim Finkelstein Abstract A new notion of bivariate aging in a competitive risk framework is introduced. Aging properties of bivariate distributions are defined by aging properties of a series system with possibly dependent components. A case of exponential marginals is considered. Sufficient conditions for a weak IFR aging (weak DFR negative aging) are derived and a number of simple examples are considered. Copyright © 2005 John Wiley & Sons, Ltd. [source] Multidimensional second order systems with controls,ASIAN JOURNAL OF CONTROL, Issue 2 2010D. Bors Abstract In the paper, a nonlinear equation with decreasing mass is considered. Sufficient conditions for the existence of solutions on the interval [t1, t2] are proved. Moreover, theorem on the stability of system and the existence of optimal control are presented. The proofs of the main results are based on variational method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] ROBUST H, CONTROL AND QUADRATIC STABILIZATION OF DISCRETE-TIME SWITCHED SYSTEMS WITH NORM-BOUNDED TIME-VARYING UNCERTAINTIESASIAN JOURNAL OF CONTROL, Issue 3 2007Zhijian Ji ABSTRACT We focus on robust H, control analysis and synthesis for discretetime switched systems with norm-bounded time-varying uncertainties. Sufficient conditions are derived to guarantee quadratic stability along with a prescribed H, -norm bound. Each of them can be dealt with as a linear matrix inequality (LMI) which can be tested with efficient algorithms. All the switching rules are constructively designed, and do not rely on any uncertainties. [source] STOCHASTIC STABILIZATION AND H, CONTROL FOR DISCRETE JUMPING SYSTEMS WITH TIME DELAYSASIAN JOURNAL OF CONTROL, Issue 3 2005Jing Wu ABSTRACT In this paper, robust stochastic stabilization and H, control for a class of uncertain discrete-time linear systems with Markovian jumping parameters are considered. Based on a new bounded real lemma derived upon an inequality recently proposed, a new iterative state-feedback controller design procedure for discrete time-delay systems is presented. Sufficient conditions for stochastic stabilization are derived in the form of linear matrix inequalities (LMIs) based on an equivalent model transformation, and the corresponding H, control law is given. Finally, numerical examples are given to illustrate the solvability of the problems and effectiveness of the results. [source] Robust H, Control Problem For General Nonlinear Systems With UncertaintyASIAN JOURNAL OF CONTROL, Issue 2 2003Jenq-Lang Wu ABSTRACT In this paper, both state and output feedback robust H, control problems for general nonlinear systems with norm-bound uncertainty are considered. Sufficient conditions for the existence of robust output feedback H, controller are provided. State space formulas for robust H, output controller are provided. [source] | ||||||||||||||||||||||||||||||||||||||||